Nikola Adžaga

activity

20142026

D (n)

-sets for several

n

12 citations · 23 across the 9 of their papers we have counts for

collaborators

11 papers

math.NT2026

Semi-stable models, local heights and quadratic Chabauty for $X_{0} (N)^{*}$

Nikola Adžaga, Maarten Derickx, Timo Keller

Quadratic Chabauty computations for $X_{0} (N)^{*}$ are complicated by local height contributions at primes of bad reduction. For squarefree $N$ , we explain a strategy for constructing…

math.NT2026

Arithmetic of elliptic curves induced by regular Diophantine triples

Nikola Adžaga

We study elliptic curves induced by regular Diophantine triples, with emphasis on their torsion subgroups. We show that an elliptic curve $E$ induced by a regular Diophantine tripl…

math.NT2026

The extensibility of the Diophantine triple ${2, b, c}$

Nikola Adžaga, Alan Filipin, Ana Jurasić

The aim of this paper is to consider the extensibility of the Diophantine triple ${2, b, c}$ , where $2 < b < c$ , and to prove that such a set cannot be extended to an irregular Diophan…

math.NT2023★ 2 cited

Asymptotics of $D (q)$ -pairs and triples via $L$ -functions of Dirichlet charaters

Nikola Adžaga, Goran Dražić, Andrej Dujella +1

Let $q$ be an integer. A $D (q)$ - $m$ -tuple is a set of $m$ distinct positive integers $a_{1}, a_{2}, ..., a_{m}$ such that $a_{i} a_{j} + q$ is a perfect square for all $1 \leq i < j \leq…

math.NT2023★ 7 cited

Computing quadratic points on modular curves $X_{0} (N)$

Nikola Adžaga, Timo Keller, Philippe Michaud-Jacobs +3

In this paper we improve on existing methods to compute quadratic points on modular curves and apply them to successfully find all the quadratic points on all modular curves $X_0(N…

math.NT2022

Rational points on hyperelliptic Atkin-Lehner quotients of modular curves and their coverings

Nikola Adžaga, Shiva Chidambaram, Timo Keller +1

We complete the computation of all $Q$ -rational points on all the $64$ maximal Atkin-Lehner quotients $X_{0} (N)^{*}$ such that the quotient is hyperelliptic. To achieve this,…

math.NT2020

The extension of the $D (- k)$ -pair ${k, k + 1}$ to a quadruple

Nikola Adžaga, Alan Filipin, Yasutsugu Fujita

Let $k$ be a positive integer. In this paper, we prove that if ${k, k + 1, c, d}$ is a $D (- k)$ -quadruple with $c > 1$ , then $d = 1$ .

math.NT2019

On the extensions of the Diophantine triples in Gaussian integers

Nikola Adžaga, Alan Filipin, Zrinka Franušić

A Diophantine $m$ -tuple is a set of $m$ distinct integers such that the product of any two distinct elements plus one is a perfect square. In this paper we study the extensibility…

math.NT2017★ 12 cited

Triples which are $D (n)$ -sets for several $n$ 's

Nikola Adžaga, Andrej Dujella, Dijana Kreso +1

For a nonzero integer $n$ , a set of distinct nonzero integers ${a_{1}, a_{2}, \dots, a_{m}}$ such that $a_{i} a_{j} + n$ is a perfect square for all $1 \leq i < j \leq m$ , is called a Diophantine $…

math.NT2016

On the extension of $D (- 8 k^{2})$ -pair ${8 k^{2}, 8 k^{2} + 1}$

Nikola Adžaga, Alan Filipin

Let $n$ be a nonzero integer. A set of $m$ positive integers is called a $D (n)$ - $m$ -tuple if the product of any two of its distinct elements increased by $n$ is a perfect square. L…

math.NT2014★ 2 cited

Automated conjecturing of Frobenius numbers via grammatical evolution

Nikola Adžaga

Conjecturing formulas and other symbolic relations occurs frequently in number theory and combinatorics. If we could automate conjecturing, we could benefit not only from speeding…

Semi-stable models, local heights and quadratic Chabauty for X0​(N)∗

Arithmetic of elliptic curves induced by regular Diophantine triples

The extensibility of the Diophantine triple {2,b,c}

Asymptotics of D(q)-pairs and triples via L-functions of Dirichlet charaters

Computing quadratic points on modular curves X0​(N)

Rational points on hyperelliptic Atkin-Lehner quotients of modular curves and their coverings

The extension of the D(−k)-pair {k,k+1} to a quadruple

On the extensions of the Diophantine triples in Gaussian integers

Triples which are D(n)-sets for several n's

On the extension of D(−8k2)-pair {8k2,8k2+1}

Automated conjecturing of Frobenius numbers via grammatical evolution

Semi-stable models, local heights and quadratic Chabauty for $X_{0} (N)^{*}$

The extensibility of the Diophantine triple ${2, b, c}$

Asymptotics of $D (q)$ -pairs and triples via $L$ -functions of Dirichlet charaters

Computing quadratic points on modular curves $X_{0} (N)$

The extension of the $D (- k)$ -pair ${k, k + 1}$ to a quadruple

Triples which are $D (n)$ -sets for several $n$ 's

On the extension of $D (- 8 k^{2})$ -pair ${8 k^{2}, 8 k^{2} + 1}$